Question

You want to buy a $240,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan for the rest.

a) How much is the loan amount going to be?



b) What will your monthly payments be if the interest rate is 6%?



c) What will your monthly payments be if the interest rate is 7%?

Answer 1

a. The loan amount will be as follows:

= Price of home x (1 - down payment)

= $ 240,000 x (1 - 0.20)

= $ 240,000 x 0.80

= $ 192,000

b. The monthly payment is computed as shown below:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 6% / 12 (Since the payments are on monthly basis, hence divided by 12)

= 0.5% or 0.005

n is computed as follows:

= 30 year x 12 months (Since the payments are on monthly basis, hence multiplied by 12)

= 360

So, the monthly payments is computed as follows:

$ 192,000 = Monthly payment x [ (1 - 1 / (1 + 0.005)³⁶⁰ ) / 0.005 ]

$ 192,000 = Monthly payment x 166.7916144

Monthly payment = $ 192,000 / 166.7916144

Monthly payment = $ 1,151.14

c. The monthly payment is computed as shown below:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 7% / 12 (Since the payments are on monthly basis, hence divided by 12)

= 0.58333333% or 0.005833333

n is computed as follows:

= 30 year x 12 months (Since the payments are on monthly basis, hence multiplied by 12)

= 360

So, the monthly payments is computed as follows:

$ 192,000 = Monthly payment x [ (1 - 1 / (1 + 0.0058333333)³⁶⁰ ) / 0.00583333333 ]

$ 192,000 = Monthly payment x 150.307574

Monthly payment = $ 192,000 / 150.307574

Monthly payment = $ 1,277.38

Feel free to ask in case of any query relating to this question